Fitted sheets for covering a mattress, are well known. Some fitted sheets such as disclosed in U.S. Pat. Nos. 2,662,234, 2,791,784, 2,857,643 and 4,461,049, provide elastic bands that extend diagonally between the corners of the fitted sheet at the underside of the mattress to aid in maintaining the fitted sheet on the mattress. Some others such as disclosed in U.S. Pat. Nos. 2,696,872 and 3,906,559, provide straps that extend crosswise between the side panels of the fitted sheet at the underside of the mattress. U.S. Pat. No. 3,114,156 discloses a fitted sheet having elastic gussets at the corners. U.S. Pat. No. 2,801,427 discloses a fitted mattress cover having some straps located adjacent the corners and which can be tied together to extend diagonally between the corners of the side panels of the mattress cover, and additional straps that can be tied together to extend crosswise of the fitted mattress cover at locations remote from the diagonally extending straps.